On spin density and hole distribution relations: valence and free valence

The formalism of the average or mean number of particles in a many-body system is applied to the "hole" distribution of many-electron molecular systems. In this way we rigorously derive expressions for the atomic valence and free valence magnitudes. It is shown that spin densities and free valence are directly related to each other in the case of maximum information state functions like ROHF (restricted open-shell Hartree-Fock) and UHF (unrestricted Hartree-Fock). For the case of correlated Cl-like expansions free valence is interpreted as a measure of the non-uniform character of the spin distribution even in the case of systems with zero total spin number. Ab initio calculations of some selected molecules are presented and discussed. (C) 1998 Elsevier Science B.V.